Question

You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is places on it. Also the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.

Answer 1

The equation for the system,

$mg-4kx=0\Rightarrow k=\frac{3000\times 10}{4\times 15\times {10}^{-2}}=5\times {10}^{4}N/m$

$T=2\pi \sqrt{M/k}=0.77$

Mass on each wheel support is $M/4=750kg$

For damping factor $x=x_o{e}^{-bt/2M}$

Now according to question, $x=x_o/2$

$\Rightarrow b=\frac{2M\ln 2}{T}$ where $T$ is time period

$T=2\pi \sqrt{\frac{m}{4K}}=0.7691s$

Now putting the value of $T$ we have

$\Rightarrow b=1351.58kg/s$